Initial stages for a steam turbine



Nov. 10, 1964 YASUO TAKEDA INITIAL STAGES FOR A STEAM TURBINE Original Filed Nov. 14, 1955 4 Sheets-Sheet 1 FIG .I PRIOR ART 'FIG.2

FIG. 7

PRIOR ART d PRIOR ART F|G.4 PRIOR ART T R A R m R P FIG FIG.8 PRIOR ART INVENTOR.

Yosuo Tokeda FIG.5 PRIoR ART Maxwell E. Sparrow ATTOR NEY- Nov. 10, 1964 YASUO TAKEDA 3,156,447

INITIAL STAGES FOR A STEAM TURBINE Original Filed Nov. 14, 1955 4 Sheets-Sheet 2 INVENTOR. F|G"3 F J YosuoTakeda BY Maxwell E.Spurrow ATTORNEY.

Nov. 10, 1964 YASUO TAKEDA 3,156,447

INITIAL STAGES FOR A STEAM TURBINE Original Filed Nov. 14,' 1955 4 Sheets-Sheet s PRIOR ART T \l PRIOR ART 013 0b; 015 o-s 1 H G |8 INVENTOR.

Yusuo Tokedo Muxwell E.Spurrow ATTORN EY.

Nov. 10, 1964 YASUO TAKEDA INITIAL. STAGES FOR A STEAM TURBINE Original Filed Nov. 14, 1955 4 Sheets-Sheet 4 L5 L0 0.8 0.6 0.5 FIG. l9

O a 0 0 w n w a o z 0 M w D 6 k K V r r o 5 1 9 0 v O \V/ 4 l 1 0 X n 5 I w 3 I 0 O s P m I 9w v 0 l I z o 0 3n iv 5 Htz/(Htd' Hta) FIG. 20

INVENTO/P. Yosuo Tokedo by Maxwell E.Sporrow ATTO R N EY.

United States Patent 3,156,447 INITIAL STAGES FOR A STEAM TURBINE Yasuo Taheda, Higashinadaku, Kobe, Japan, assignor to Kawasaki Jukogyo Kabushiki Kaisha (Kawasaki Dockyard Co., Ltd.)

Continuation of application Ser. No. 546,759, Nov. 14,

1955. This application Dec. 22, 1960, Ser. No. 77,771

1 Claim. (Cl. 253-69) This invention relates to the initial stages of a steam turbine; that is to say, to the stages which, by the opening and closing of the nozzle valves at the inlet of steam flow, have a direct relation to the control of the number of revolutions of the turbine. The initial stages do not include what are commonly called stages which have no direct relation between the opening of the nozzle valves and the number of revolutions of the turbine.

This application is a continuation of co-pending application Serial No. 546,759, filed November 14, 1955, now abandoned.

This invention actually consists of two impulse stages, i.e., the first impulse stage in which a row of nozzles of the partial admission type is arranged on the inner wall of the casing and the co-operating row of the moving blades on the rotor, and the second impulse stage in which a row of nozzles of the partial admission type is formed in a diaphragm which is fixed on the inner face of the turbine casing and is provided with a labyrinth seal to shut off steam flow through the interstice between the rotor and the said diaphragm. The initial stages of this invention are so planned that the heat drop across the nozzles of the first stage is 1.5 to 3 times as great as that across the nozzles of the second stage within the limit that the velocity of the steam at the nozzle outlet of the first stage does not exceed sonic velocity and that, as by the above mentioned planning of the heat drop, the direction of the steam flowing out of the moving blades of the first stage into the nozzles of the second stage is deviated from that of the centre line of the rotor shaft, the inlet of the nozzles of the second stage being so shaped as to correspond to this deviated flow of steam.

The invention will now be more fully described, by way of example, with reference to the accompanying drawings in which:

FIG. 1 is a longitudinal section of a part of steam turbine equipped with the well-known Curtis stage;

FIG. 2 is a developed view of the periphery of the Curtis stage shown in FIG. 1;

FIG. 3 is a diagram including curves showing changes in the pressure and velocity of steam in the Curtis stage;

FIG. 4 is a longitudinal section of a part of a steam turbine equipped with the well-known Rateau stage;

FIG. 5 is a developed view of the periphery of the Rateau stage shown in FIG. 4;

FIG. 6 is a diagram including curves showing changes in the pressure and velocity of steam in the Rateau stage;

FIG. 7 is a vector diagram of steam velocity in the Curtis stage;

FIG. 8 is a vector diagram of steam velocity in the Rateau stage;

FIG. 9 is a longitudinal section of a steam turbine equipped with the initial stages of this invention;

FiG. 10 is a developed view of the initial stages of this invention shown in FIG. 9;

FIG. 11 is a diagram including curves showing changes in the pressure and velocity of steam in the initial stages of this invention;

FIG. 12 is an enthalpy-entropy diagram of steam in the initial stages of this invention.

FIG. 13 is a vector diagram of steam velocity in the first stage of the initial stages of this invention;

"ice

FIG. 14 is a vector diagram of steam velocity in the second stage of this invention;

FIG. 15 is a fragmentary view to an enlarged scale of a part of the turbine shown in FIG. 9;

FIG. 16 is a diagram with a curve showing velocity ratio v efiiciency in a well-known impulse turbine;

FIG. 17 is a view showing the construction of the principal part of the initial stages of this invention;

FIG. 18 is a diagram with curves showing the efficiency of the initial stages of this invention in contrast with that of a well-known one;

FIG. 19 is a diagram showing that when the heat drop ratio Hz /Ht is selected from 1.5 to 3.0, the total losses incurred with these initial stages are at a minimum in elalmost all cases; and

HG. 20 is a diagram, showing the reason why the total losses are the smallest in the range of 1.5 to 3.0 of the heat drop ratio H t H Q.

The velocity stage common in use in steam turbines heretofore is either the Curtis stage or the Rateau stage.

The Curtis stage is a type in which, as shown in FIGS. 1 to 3, the pressure P drops in the first nozzles 0 alone and the velocity w reaching its, highest value at the outlet of the nozzles a, passes through the first row of moving blades b and, turning at the stationary blades c, passes through the second row of moving blades d, and thus it is converted to motive power. The Rateau stage is a type in which pressure P drops as shown in FIGS. 4 to 6, in the first nozzles a alone as is the case with the Curtis stage, but it has only one row of moving blades b Where the energy of velocity w is converted to motion.

In comparing the natures of the Curtis and Rateau stages in the diagrams of vectors in FIGS. 7 and 8, it should be noted that in both diagrams C denotes the absolute steam velocity, w the steam velocity relative to the moving blades, U the rotor circumferential velocity of the moving blades, and the numerals l, 2, 3 and 4 sufiixed to the right foot of each letter show successively the steam velocity at the inlet, and that at the outlet, of the moving blades of the first stage, and the steam velocity at the inlet, and at the outlet of the moving blades of the second stage, and the marks and at the right shoulder of each letter show the velocity of the Curtis stage and that of the Rateau stage, respectively. Generally speaking, it is well-known that the efiiciency of the Curtis stage is the best and that the Rateau stage is the best when the Curtis stage works with the velocity ratio U'/C about 0.23, the Rateau stage with the velocity ratio U"/C about 0.47. Accordingly, on the assumption that, with their velocity ratios chosen at these values, both the rotor circumferential velocities U and U" of the moving blades of the Curtis and Rateau stages have the same velocity U, the steam velocity at the inlet of the moving blades of theCurtis stage, i.e.

U I C ma;

is twice as much as that at the inlet of the moving blades of the Rateau stage, i.e.

and this shows that the Curtis stage can cope with about four times as much heat drop as the Rateau because heat drop corresponds to the square of the velocity. And its capacity for coping with a great heat drop is characteristic of the Curtis stage, and owing to the capacity, it has the following advantages over the Rateau stage when coping with the same heat drop; (a) it can have a rotor smaller in diameter, the smaller rotor resulting in a turbine as a whole smaller in size than the Rateau stage, and (b) the manufacture of the rotor is easy and the rotation loss is small. The Curtis stage is inferior in ordinary cases to the Rateau stage in efliciency, however, due to the conditions that the heat drop is so great that the steam velocity at the nozzle outlet is too high, exceeding sonic velocity in most cases and the shock loss increases, and the steam flow turns four times while the Rateau stage has two turnings of the steam while the turning angle is great in the Curtis stage at the first moving blade row.

On the other hand, the Rateau stage, though it is superior to the Curtis stage in efliciency as mentioned above, has the defect that, as the velocity of steam produced by the heat drop at the nozzles a is to be taken up by these moving blades b alone, it is necessary to make the pitch circle of the moving blades b of the first stage especially large as shown in FIG. 4 with very complex ditficulties in the construction of the turbine casing and of the rotor and with the cost of manufacture correspondingly expensive. It also has the defect that the larger the pitch circle of the moving blade b is, the smaller becomes the radial height of the blade b itself to a fixed fiow of steam, so that the loss, in this part increases.

In the Curtis stage shown in FIGS. 1 to 3, a known method is to provide a slight range of percentage of heat drop in the stationary blades to obtain an efiiciency which is very good when compared with that of a common Curtis stage, but with this method the heat rop across the stationary blades 0 is a seventh to a tenth of the heat drop in nozzles a of the first row and only a slight improvement can be attained in efliciency by making the steam flow through the stationary blades 0 somewhat accelerated, the mitigation of the heat drop in the nozzles a being very slight, and aforesaid defect of the Curtis stage is still not removed, i.e. the defect that the velocity of steam on issuing from the outlet exceeds sonic velocity and the shock loss is great.

This invention removes the defects of the aforesaid well-known stages of turbines, and advocates a new type of initial stages which have a very high efiiciency.

FIG. 9 is a longitudinal section showing a steam turbine equipped with the initial stages of this invention. Steam enters the steam chest 5 from an inlet 4, then flows to the moving blades 7 through the nozzles 6 of the first stage which are fixed on the wall of the casing, then flows out of the nozzles 8 of the second stage which are formed in a diaphragm that has a labyrinth seal 21, passes through the moving blades 9 of the stage and then goes alternately through the rest of the nozzles 16 and blades 11 of the remaining stages till it goes out of the turbine from the exhaust outlet. The diaphragm 29 is fixed at its outer circumference to the casing of the turbine and is provided with a labyrinth seal 21 to prevent steam from flowing through the interstice between the rotor and the said diaphragm.

In the above construction, when the volume of inflowing steam is controlled by opening and closing of the nozzle valves attached to the inlet of the nozzles 6, the velocity of the turbine is determined by these first and second stages.

When the constructions of the Curtis stage shown in FIG. 1 and the initial stages of this invention are compared:

(a) The Curtis stage and the initial stages of this invention have both two sets of moving blades.

(b) In the Curtis stage stationary blades are arranged between the two sets of the moving blades and the said stationary blades do not expand the steam and consequently they digest no heat drop, while in the initial stages of this invention nozzles are arranged between the two sets of the moving blades, and the said nozzles have a heat drop across them.

It is also the practice in the latest Curtis turbines to provide in the initial stages a 5% to 10% range of percentage of heat drop. The difference between the Curtis stage in which percentage of heat drop is being given to the stationary blades, the above mentioned range of percentage of heat drop, and the initial stages of this invention is essentially the difference in the range of percentage of heat drop with respect to the distribution of the heat drop. The heat drop across the second nozzle of the initial stages of this invention amounts to a range of percentage of heat drop of 25% to 40%. This difference in the range of percentage of heat drop brings the following characteristic in the construction of the initial stages of this invention.

(c) The Curtis stage has no diaphragm between the two moving blade disks While the initial stages of this invention include a diaphragm 26 which separates the chamber of the first stage from that of the second stage in order to preserve pressure in the chamber of the first stage.

When the construction of the Rateau pressure stage shown in FIG. 4 and the initial stages of this invention are compared:

(a) The Rateau pressure stage has one set of moving blades while the initial stages of this invention include two sets of moving blades, and

(b) In the Rateau pressure stage the pitch circle diameter of the moving blades is very large as it has to digest a considerably larger heat drop by the one set of moving blades.

The initial stages of this invention include as is explicit in the developed drawing of FIG. 10, a type of partial admission in which the nozzles 6 and 8 are fixed only on a part of the circumference of the turbine. The partial admission of the nozzles 6 of the first stage is due to the governing nozzle valves arranged for this purpose at the steam inlet to the turbine. The nozzles 3 of the second stage are also a type of partial. admission in order to attain an efficicnt control by receiving the partial admission of the steam directly as it flows out through the first stage.

FIG. 11 shows the changes of steam pressure P and steam velocity w of the initial stages of this invention. The steam pressure P changes step by step in the initial stages of this invention as shown in the curve of FIG. 11, this being due to the expansions which take place respectively in the nozzles 6 and 8. In the Curtis stage and the Rateau stage expansion takes place in one row of the nozzles and the pressure curve changes in one step as shown in FIG. 3 and FIG. 6. The change of steam velocity in the initial stages of this invention have a characteristic ditferent from those of the Curtis stage and of the Rateau stage. In FIG. 11, the curve of steam velocity w comprises two peaks while in FIG. 3 and PEG. 6 the curve w is only made up of one peak.

The heat drop in each stage changes as shown in the enthalpyentropy diagram, i.e. the i-s diagram in FIG. 12. In FIG. 12, steam expanding adiabatically in the first stage nozzles 6 from the pressure P to the pressure P changes its state from the point a to the point I), but due to the losses in the nozzles 6 and the moving blades 7, it is, at the outlet of the first stage moving blades 7, in a state of the point c on the pressure line P and then expanding again adiabatically in the nozzles 8 of the second stage, it comes to the state of the point d. The line ab corresponds to the heat drop Ht, KcaL/kg. in the first stage and the line 0-0. corresponds to the heat drop Ht, K cal/kg. in the second stage, and as both of them are of impulse stages, the steam expands in the nozzles 6 and 8 alone. FIGS. 13 and 14 are respectively diagrams of vectors of the steam velocities in the first and the second stage produced by the aforesaid heat drops Ht, and H1 and in this figure, C C and C C denote respectively the absolute velocities at the inlets and the outlets of the moving blades 7 and 9; W W and W W denote. respectively the relative velocities at the inlets and the outlets of the moving blades 7 and 9, U denotes the rotor circumferential velocities of the moving blades 7 and 9 which have equal pitch circle diameters and a and a denote the nozzle angles.

In this invention, the relation between the heat drops Ht and Ht; is, as mentioned above, chosen so that Hi is 1.5 to 3 times Hi i.e. the range of heat drop of the second nozzles Ht /(Ht -|-Ht is chosen as 0.25O.4.

The reasons why this ratio or" heat drop is chosen are as follows:

(a) The larger the heat drop is chosen in the first stage, the lower falls the pressure P at the outlet of the nozzles of the first stage and consequently the smaller become the external leakage lossesthe leakage losses from the labyrinth 14 shown in FIG. -with great advantage;

(b) But on the other hand when the heat drop of the first stage becomes too big, the steam velocity at the outlet of the nozzles exceeds sonic velocity as is the case with the Curtis stage, wheich causes shock loss to increase.

(0) With due consideration of these two opposite phenomena the range of the ratio of the heat drops is chosen between 1.5 and 3.0 where the best efficiency can be obtained.

The above mentioned ratio Ht /Ht of heat drop is chosen within the limit that steam velocity at the outlet of the nozzles of the first stage does not exceed sonic velocity.

FIG. 16 is an efiiciency curve of a common impulse stage with what is called the velocity ratio 1 between the steam velocity C on issuing from the nozzles and the circumferential velocity U of the rotor as the abscissa and the efificiency m as the ordinate, and in the curve, as shown plainly in this figure, the efficiency reaches its highest at the point Where the value of the velocity ratio 1/ is between 0.45 and 0.48. When in the well-known related formula:

the velocity ratio v of the second stage of the initial stages of this invention is chosen to that T7 91.s /17i; the velocity ratio 11 of the first stage is, due to the relation of the aforesaid Ht =1.5 to 3 times Ht In short, the ratio 11 of the first stage turns out to be between 0.28 and 0.4 and this gives a poor efiiciency according to the curve of FIG. 16. The reason Why efficiency becomes poor when this velocity ratio is small in value is that, in a small velocity ratio, the velocity on issuing from the moving blades, i.e. the value of the velocity C at the outlet of the moving blades 7 in the vector diagram becomes great in FIG. 13 as the result of the ratio of heat drop and its energy is also great. Thevelocity C also follows an inclined line instead of a direction perpendicular to the velocity U and the energy exhausted is great and the efiiciency is thereby lowered. In the initial stages of this invention, as shown in FIG. 17', the inlet edges of the second stage nozzles 8, are shaped to correspond with the velocity C as it issues from the moving blades 7 of the first stage which considerably deviates from the axial direction. The nozzles 8 of the second stage with these curved shapes at their inlet edges can collect and utilize the energy of C With the detailed description given above concerning the features of the initial stages of this invention, it can be practically realized that the initial stages of this invention remedy the defects of the well-known Curtis and Rateau stages and can achieve an excellent and superior 6 eificiency. Disregarding the losses at the nozzle and the moving blades and supposing that the steam velocity C issuing from the moving blades 7 of the first stage is collected by the nozzles of the second stage, the loss of the initial stages of this invention as a whole is nothing but the velocity C on issuing from the moving blades of the second stage, and i standing for the efficiency of the initial stages, We get Ht +Ht (l) and here suppose t =2Ht and arrange the Formula 1 with C =91.5 /Ht and we get and solve C by the well-known theory of turbines with impulse blades of symmetrical form and we get and as for C in the above formula, it is i 2 C =C [l+4 4 (30501 (3) with ' The relation between 11 and 1/ in the above formula,

through the following relatedformulae:

In this formula, estimate 1 in various values of 11 with oc =oz =I4 and show the relation between 11 and 1 in a diagram, and the result approaches to the char-v acteristic curve A in FIG. 18. The curve B in the figure is an efiiciency curve got with mg -14 in (Note: v Velocity ratio in a single stage. zle angle.)

na -NOZ- which is an efficiency formula of the well-known single stage, i.e. the Rateau stage. In the efliciency characteristic of the Curtis stage, it is well-known that except the velocity ratio that gives the highest efficiency, the tendency of its characteristic is of a parabola type similar to the B curve of the single stage. When the curves A and B are compared, the curve A of the efficiency characteristic of this invention is superior by far to the curve B as regards the best efficiency, and as the curve A has an easier slope than the curve B, it is evident that the curve A has a very excellent efficiency at other partial loads than that corresponding to the velocity ratio which shows the best efficiency.

' In the above calculations of efi'iciency of the initial stages of this invention such losses as the nozzle loss, the

blade loss, the rotation loss and the leakage loss have not been considered to make the calculation simple, but in the Rateau stage the rotation loss is great as the rotor has a large diameter and the shaft becomes thick in proportion to the enlargement in the size of the diameter of the rotor. If the diameter of the rotor and that of the shaft are made small, the pressure after the first stage becomes too great and causes the leakage loss to increase, and, taking these disadvantages into consideration, it has a characteristic inferior to what is shown in the efficiency curve B, while in the Curtis stage, shock waves are caused due to the velocity which is so great on issuing from the nozzle as to exceed sonic velocity. The nozzle loss and the blade loss increase considerably, and when these losses are taken into consideration this stage may be regarded as with the Rateau stage as having a much less efliciency. It is understood, therefore, that when the aforesaid losses are taken into consideration, the initial stages of this invention have greater efliciency than the well-known Rateau and Curtis stages with a difference between them greater than what is shown by the two curves A and B in FIG. 18. As for the above mentioned Curtis stage, even the stage which is devised to have a slight degree or" reaction in the stationary blades does not differ, though some improvement may be expected from the accelerated steam flow through the stationary blades, from the common Curtis stage in these respects that the heat drop acrossthe nozzles of the first row is as great as ever, that the velocity of steam at the nozzle outlet is still so great as to exceed sonic velocity and that the flow turnings increase and the a turning angle is great, and thus not only in respect of best efficiency does it not come up to the initial stages of this invention but in other partial loads it is inferior by far to the initial stages of this invention. In the construction of the Curtis stage, as there is no diaphragm between the moving blades of the first row and the stationary blades of the second row, the result is that the bigger the heat drop across the stationary blades, the greater is the leakage loss at the tips of the stationary blades and the more the loss as a whole increases.

In short, the initial stages of this invention have a particularly excellent and marked efficiency when compared with the well-known velocity stages not only in the velocity ratio which brings about the best efiiciency but also in other partial loads with various advantages.

FIG. 19 is a diagram showing when 1.5 to 3.0 of the heat drop ratio Ht /Ht is selected, total losses incurring with this type of regulating stages are at a minimum in almost all cases. On this diagram, total losses AL consist of nozzle losses of first and second stage, blade losses of first and second stage, friction losses of rotating discs of first and second stage, discharging losses of second stage, leakage losses from the diaphragm seal between first and second disc and leakage loss of external packing seal.

Abscissae of this diagram are the heat drop ratio Ht /Ht and the reaction degree of the second nozzles Ht /(Ht -i-Ht and the parameter P /HPXN means size of turbine. While P is the initial pressure of the turbine, HP is the horsepower of the turbine, N is the number of revolutions of the turbine.

Range I, shown in FIG. 19 corresponds to conventional stages, and especially the point of H t /Ht =oo or corresponds to a pure Curtis stage.

Range II corresponds to the regulating stage of this invention, and Range III corresponds to the regulating stage simply combined of two sets of Rateau stages. Dotted line IV in FIG. 19 shows the tendency of minimum total losses.

As can be seen from this figure, the range of minimum total losses is covered by the range of the heat drop ratio 1.5 to 3.0 in almost all cases.

The range of the figures for the parameter P /HPXN in FIG. 19 is selected in concurrence with actual turbines as illustrated by the following examples:

Example 1 PO=2O kg./cm. abs, HP=3,000HP, N:8,000 r.p.m. PO/HPXN=0.825 10- Example 2 Example 3 1 ,:140 kg/CIIL abs., HP=136,()00HP mw.), N=3,600 r.p.m. P0/HPXN=0.287 10 FIG. 20 is a diagram showing that we can divide the total losses of the regulating stage AL into two groups.

One group AL consists of nozzle losses, blade losses and discharge losses of the second stage.

The amount of AL is especially influenced by the total deviation angle of nozzles and blades. These losses AL therefore, become larger for Curtis stages and smaller for Rateau stages.

However, the other group AL which consists of friction losses of discs, leakage losses of diaphragm sealing and leakage losses of external packing has an opposite tendency compared with AL The reason why the loss AL has the opposite tendency is as follows: AL is influenced by the pressure of the first stage outlet P or by the pressure of the second stage outlet P2.

At a Curtis stage, P and P are smaller than shown in FIG. 20, thus AL is smaller. Contrariwise, at a Rateau stage P and P are larger, thus AL is larger.

It is clear that when such stages are assumed, it has to be considered that the total losses AL consist of AL and AL In this respect, it is emphasized that the total losses AL occurring within the range of Curtis stages and within the range of Rateau stages are not smaller than the AL within the range of the regulating stages of this invention. As a matter of fact, the total losses AL for the regulating stages of this invention-medium heat drop rangeare the smallest. The calculations for FIG. 19 and FIG. 20 are based on well-known principles and experimental data.

I claim:

In a rotary steam turbine having a casing and a rotor rotatably arranged in said casing, said rotor having a shaft and having more than two turbine wheels secured thereto, said turbine wheels having blades thereon; the first two stages in said turbine comprising a first impulse stage and a second impulse stage, each of said impulse stages having a row of fixed steam nozzles of the partial admission type, said row of steam nozzles of said first impulse stage being arranged on the inner wall of said casing for cooperation with said blades of a first turbine wheel, a diaphragm arranged between said first turbine Wheel and a second turbine wheel of said plurality of turbine wheels, a labyrinth seal formed between said diaphragm and said rotor of said turbine for preventing the flow of steam through the existing interstice between said diaphragm and said rotor, said row of steam nozzles of said second impulse stage being arranged in said diaphragm for cooperation with said blades of said first turbine wheel and with said blades of said second turbine wheel, the steam flow emerging from said first impulse stage deviating from the center line of said rotor shaft under design conditions, and said steam nozzles of said second impulse stage having inlet edges arranged corresponding to said deviated steam flow, said first two stages being constructed in such a manner that when steam is flowing in said turbine and said turbine is operating under design conditions said first impulse stage has a heat drop of substantially 1.5 to 3 times the heat drop in said second References Cited in the file of this patent UNITED STATES PATENTS Vauclain Aug. 12, 1913 OTHER REFERENCES Sorensen, H. A.: Gas Turbines, N.Y., Ronald Press, 1951, p. 294.

Lee, J. F.: Theory and Design of Steam and Gas Turbines, N.Y., McGraw-Hill, 1954, pp. 7-9.

Croft, Terrell: Steam Turbine Principles and Practice, N.Y., McGraw-Hill, 1923, pp. 36-38.

Steam Turbine Principles and Practice, Terrell Croft, editor, 1st ed., 1923, published by McGraw-Hill Book Co., Inc., N.Y., pages 55-58.

Theory and Design of Steam and Gas Turbines, John F. Lee, 1954, published by McGraW-Hill Book Co., Inc., N.Y., page 192.

Steam Turbines and Their Cycles, J. Kenneth Salisbury, 1950, published by John Wiley and Sons Inc., N.Y., page 560.

Steam, Air, and Gas Power, 5th edition, 1955, John Wiley and Sons Inc., New York, pages 263-267. 

